Do Output Contractions Cause Investment in

Fiscal Capacity?

Christian Gillitzer∗

Reserve Bank of Australia

April 2015

Abstract

This paper shows that an economic slump can induce a government toinvest in fiscal capacity. Large negative income shocks stress the revenue-raising capability of narrow tax bases, making an increase in tax base breadthdesirable relative to its fixed implementation cost. A broader tax base enablesrevenue to be raised at lower tax rates, which reduces the efficiency cost oftaxation. The behavior of U.S. state governments during the Great Depressionsupports the model: states experiencing larger than average negative incomeshocks were more likely to adopt a retail sales tax than were states experienc-ing smaller than average income shocks.

JEL Codes: E62, H7, H21.

∗I am grateful to my dissertation committee for their guidance and encouragement: Joel Slemrod,Matthew Shapiro, Jim Hines and Martin Schmalz. I am also grateful to Ethan Ilzetzki for detailedand insightful comments on an earlier draft, Ron Cheung (discussant), Greg Kaplan, Nalini Prasad,and seminar participants at the National Tax Association Conference 2013. This paper is a revisedversion of the first chapter of my dissertation at the University of Michigan. The views representthose of the author and should not be attributed to the Reserve Bank of Australia. Contact: EconomicResearch Department, Reserve Bank of Australia, 65 Martin Place, Sydney, NSW, 2000. Email:gillitzerc@rba.gov.au.

1

1 Introduction

Much of the modern public finance literature takes the set of tax bases as exoge-

nously fixed, and studies the optimal tax rate to levy on those bases. But a defining

feature of economic development is growth and compositional change in the set of

tax bases used to raise revenue. In developed economies, modern consumption and

income tax bases have largely replaced comparatively inefficient trade, seignorage,

and occupational licensing taxes. These tax base changes have reduced the effi-

ciency cost of raising revenue and facilitated the growth of government in developed

economies (Becker and Mulligan, 2003). For developing economies, understanding

the determinants of tax base expansion is important because limited ability to raise

revenue at tolerable efficiency cost is widely seen as a barrier to economic growth

in the developing world today (Besley and Persson, 2013).

The adoption of the modern fiscal state in developed economies proceeded in

three waves. Income taxes began to be adopted in the late 1800s, income-tax with-

holding and an extension in the reach of the income tax to wide sections of the

population occurred in the early to mid 1900s, and the adoption of Value Added

Taxes occurred in the post World War II years (Besley and Persson, 2013).1 In

a sample of mostly high-income countries tracked by Besley and Persson (2013),

each country had introduced an income tax with withholding by the year 2000, and

all but the U.S. had adopted a VAT. Governments used these new tax bases to in-

crease tax revenue as a share of GDP from on average less than 10 percent in 1900

to around 25 percent by the year 2000.2

1The first income tax was introduced in Great Britain by William Pitt the Younger in 1798.2See Figure 5 in Besley and Persson (2013). Their sample of countries is: Argentina, Australia,Brazil, Canada, Chile, Columbia, Denmark, Finland, Ireland, Japan, Mexico, the Netherlands, New

2

A growing literature models these tax base changes as purposeful investments

in fiscal capacity. The central empirical fact that much of the literature on state

capacity seeks to explain is the coincidence of external wars and the upgrading

of fiscal capacity. A glance at U.S. history illustrates this correlation: the first

U.S. income tax was proposed during the War of 1812 (although the war ended

before the tax was instituted); income taxes were imposed on a small number of

taxpayers during the U.S. Civil War; the estate tax was introduced during World War

I; and during World War II withholding for wage and salary income was introduced,

strengthening the ability of tax administrators to enforce the income tax code. The

interdependence between wars and fiscal capacity is captured in historian Charles

Tilly’s (1975, p. 42) famous words “War made the state, and the state made war.”

In a seminal body of research, Besley and Persson (2009; 2010; 2013) and

Besley, Ilzetzki and Persson (2013) present a framework in which wars catalyze

investment in fiscal capacity. Their model highlights the role of political frictions

limiting investment in state revenue-raising capacity. External wars act as a stim-

ulant to investment in fiscal capacity in their framework because military spending

is “an archetypal public good representing broadly common interests for citizens”

(Besley and Persson, 2009, p. 1218). Their framework assumes non-distortionary

lump-sum taxes, with fiscal upgrading corresponding to investment in compliance

infrastructure that limits evasion and avoidance behavior. In reality, upgrading of

fiscal institutions includes both improvement in compliance infrastructure and the

adoption of new tax bases, both of which can lower the efficiency cost of raising

revenue.

Zealand, Norway, Sweden, Switzerland, the United Kingdom, and the United States.

3

This paper provides a new explanation for investment in fiscal capacity, studying

the role of macroeconomic income shocks. Confronted with a decline in income, a

government with limited ability to borrow must either raise taxes or cut spending.

In general, government spending does not fall proportionately with income in an

economic slump, in part because demand for some government activities do not

vary proportionately with income. This creates a revenue shortfall that must be

covered by either raising the tax rate on existing narrow tax bases, or undertaking a

tax base broadening reform, enabling the taxation of a broader set of goods. Raising

tax rates on existing tax bases raises revenue but increases deadweight loss, which

is convex in the tax rate. For a sufficiently large fall in income, it is optimal to incur

the fixed cost to undertake a tax base broadening reform. Taxing a wider range

of economic activity at lower tax rates permits raising a given amount of revenue

at lower efficiency cost. Macroeconomic income fluctuations are transitory but,

when the fixed cost incurred to upgrade fiscal capacity is large, improvements in

fiscal capacity can be enduring. The fixed cost to increase tax base breadth includes

all the expenses required to build a tax administration to collect and enforce tax

payments on a new tax base.

I formalize this intuition with a model in which a benevolent government pro-

vides a public good by taxing either a narrow share of private consumption goods

at a high tax rate or a broad set of goods at a low tax rate. The broader is the tax

base—corresponding to a higher level of fiscal capacity—the lower is the marginal

efficiency cost of raising tax revenue, because a broader tax base permits the same

amount of revenue to be raised at a lower tax rate. The model deliberately abstracts

from political-economy considerations to investigate the power of a model assum-

4

ing a benevolent government to explain upgrading in fiscal capacity.

The model’s key predictions are tested by studying the behavior of U.S. state

governments during the Great Depression. This time period and set of governments

provide an excellent setting to examine the effect of an economic slump on tax base

expansion. The decline in income was large, with per capita U.S. real GDP falling

by 29 percent between 1929 and 1933. There was also substantial heterogeneity

in the size of income shocks experienced across states. Because U.S. state govern-

ments had limited ability to borrow, they quickly faced a choice between raising

tax rates on existing tax bases or expanding tax base breadth to address revenue

shortfalls.

Over the period of the Great Depression, U.S. state governments profoundly

changed their tax structure. In 1929, none of the 48 U.S. state governments levied

a broad-based consumption tax. But during the 1930s, 28 states introduced a retail

sales tax, of which 22 ultimately became permanent. Tax rates were initially low,

but retail sales taxes quickly became an important source of revenue. States adopt-

ing a permanent retail sales tax in the 1930s raised on average about one-fifth of

total tax revenue from the retail sales tax by 1942. Spending and revenues evolved

similarly for U.S. state governments that did and did not introduce a retail sales

tax, implying that state governments that introduced a retail sales tax were able to

raise revenue at lower tax rates, and thus at lower efficiency cost, consistent with

the model.

The cross-sectional pattern of tax base adoption is also consistent with the

model. The average fall in per capita personal income between 1929 and 1933

was 7 percentage points larger for states that adopted a retail sales tax in the 1930s

5

than those that did not. Each 10 percentage point fall in income between 1929 and

1933 is estimated to have raised the probability of a U.S. state government intro-

ducing a retail sales tax in the 1930s by 16 percent. This relationship is robust to a

variety of controls.

This paper’s model and empirical findings invite a reconsideration of the factors

responsible for the correlation between wars and tax base expansion. The political-

economy literature emphasizes the common interest nature of military spending

as the catalyst for wartime investment in fiscal capacity. But both the magnitude

as well as the nature of spending changes in wartime. High levels of spending in

wartime stress the revenue raising capacity of narrow tax bases, making an increase

in tax base breadth desirable on efficiency grounds alone. It is therefore unclear

whether it is the change in the composition of spending or the magnitude of spend-

ing that is the main factor responsible for wartime investment in fiscal capacity.

Economic slumps provide an opportunity to determine whether a rise in the distor-

tionary cost of taxation — absent changes in military spending — is sufficient to

induce investment in fiscal capacity. The adoption of retail sales taxes by U.S. state

governments during the Great Depression indicates that a rise in the distortionary

cost of taxation alone is a powerful motive for tax base expansion.

This paper is also related a literature that studies the optimal use of debt to

smooth fluctuations in revenue needs. Barro (1979) shows that, if possible, a gov-

ernment should borrow and lend to minimize tax-rate variation, thereby reducing

the efficiency cost of taxation, which is convex in the tax rate. This behavior is often

described as tax-rate smoothing. In my model, governments are assumed to have a

balanced budget requirement, and so must match revenues and expenses period by

6

period. But unlike Barro (1979), fiscal capacity is endogenous. I rule out the use

of debt as a means to minimize the distortionary cost of taxation because U.S. state

governments had limited ability to borrow to fund non-capital related expenditures.

This does not alter the proposition that a sufficiently large fall in income induces

a tax base broadening reform. Incurring debt provides a means to postpone the

collection of revenue, and spread repayments over time, but absent default govern-

ments must ultimately run a budget surplus to make up for past revenue shortfalls.

The larger are net debt repayments, the greater is the revenue requirement relative

income, and the more desirable is a tax base broadening reform.

Although the role of wars is a central feature of the literature, a number of other

factors affecting incentives to invest in fiscal capacity have been explored. Political

turnover and the cohesiveness of institutions has been shown to affect the incen-

tives for politicians to invest in fiscal capacity (Besley and Coate, 1997). A lack

of social cohesion, such as ethnic fragmentation, makes incumbent politicians un-

willing to invest in fiscal institutions that can be used by future governments to

redistribute money to disfavored groups (Alesina et al., 1999). More generally,

political turnover makes politicians undervalue the future benefits of higher fiscal

capacity, and creates incentives for incumbents to tie the hands of their successors

(Persson and Svensson, 1989). Other work argues that structural change occur-

ring during the process of development changes the types of taxes that are feasible

and desirable. For example, increased employment in formal sector firms enables

information reporting and withholding of income taxes at source (Kleven et al.,

2009), while increases in financial transactions through banks provides records for

tax inspectors to enforce tax laws (Gordon and Li, 2009). Particularly in develop-

7

ing countries, foreign aid flows (Besley and Persson, 2013) and resource revenues

(Jensen, 2011) have been found to be associated with lower levels of fiscal capacity.

But, to the best of my knowledge, the role of macroeconomic income shocks has

not previously been considered.3

The remainder of the paper proceeds as follows: Section 2 lays out and dis-

cusses a formal model endogenizing the upgrading of fiscal capacity, Section 3

uses the experience of U.S. state governments during the Great Depression to test

the model’s key predictions, Section 4 discusses the empirical results in light of the

model, and Section 5 concludes.

2 Model

2.1 Overview

The model assumes a government that raises revenue via a distortionary tax to pro-

vide a public good. It is based on Yitzhaki (1979), but differs in a number of

important ways.4 Households receive a time-varying income endowment and con-

sume a continuum of private goods, for which the government chooses both the tax

rate and the breadth of the tax base (the set of taxed commodities). A broader tax

base corresponds to a higher level of fiscal capacity, and these two terms are used

interchangeably. Cobb-Douglas utility is assumed because with these preferences

3See the recent handbook chapter by Besley and Persson (2013), and the references therein, for amore complete account of the existing literature.

4Wilson (1989) extends the Yitzhaki (1979) model to consider different elasticities of substitutionbetween taxed and untaxed goods. Slemrod and Kopczuk (2002) extend the Yitzhaki (1979) modelto include heterogeneity in income-earning ability among taxpayers and a concave social welfarefunction.

8

a uniform rate on all taxed goods is optimal, permitting the analysis to use a single

tax rate and thus sidestep the issue of differentiated tax rates among goods, which

is not a central issue in this context.

An increase in tax base breadth lowers the excess burden of taxation, because

there are fewer untaxed goods for taxpayers to substitute toward, but raises admin-

istrative cost, which is assumed to be increasing in tax base breadth. As an example

of the relationship between tax base breadth and administrative cost, expanding the

sales tax base to include services is widely believed to raise administrative cost be-

cause service transactions are generally more costly to observe, and therefore to

tax, than are goods transactions. Because U.S. state governments were unable to

meaningfully borrow to fund non-capital expenditures, I assume the government

has a per-period balanced budget requirement. The following subsection begins the

formal description of the model.

2.2 Preferences, Income Endowment and Tax Base

There is a representative consumer who has Cobb-Douglas utility over a continuum

of privately consumed goods, ci,t , and a single public good, Gt consumed in time t:

Ut =

ˆ 1

0αilog(ci,t)di+φ log

(Gt − G

), (1)

where φ parameterizes the representative consumer’s preference for the public good

relative to privately consumed goods. The sum of the parameters αi is normalized

to unity,´ 1

0 αidi = 1. At an optimum for the consumer, the parameter αi is equal to

the consumer’s expenditure share of income on good i ∈ [0,1]. The representative

9

consumer receives an exogenous income endowment yt over the domain yt ∈ [0,∞).

For simplicity, I assume that income shocks are independent and identically dis-

tributed: yt ∼ iid(y,σ2

y).5 The assumption of an endowment economy means that

there is no labor/leisure trade-off, and that leisure is not included in the set of pri-

vately consumed goods. As a consequence of the representative agent assumption,

there are no differences in income or time preference across households that would

give rise to borrowing or lending between households, and the representative con-

sumer spends all their income each period. For simplicity, each state is assumed to

be a closed economy, so there is no borrowing or lending outside the state. There is

a level of mandatory spending G, such as spending on law and order, that does not

vary with income.6

The set of goods i ∈ [0, It ] are subject to a uniform tax rate, and the remaining

set of goods i ∈ (It ,1] are not taxed. The larger is the index of taxed goods, It , the

broader is the tax base because a wider set of commodities is subject to tax. The

expenditure share of taxed goods is b(It)≡´ It

0 αidi and, because bt is a monotonic

transformation of It , the planner can equivalently set the breadth of the tax base by

choosing bt or It . Normalizing the exogenous pre-tax price of all goods to unity,

households face the price pi,t = 1/(1− τt) for goods i ∈ [0, It ], and pi,t = 1 for

goods i ∈ (It ,1].

5Allowing for serial correlation in income would not alter any of the model’s key predictions.6For simplicity the model does not incorporate trend growth in incomes, which is not important inthis context.

10

2.3 Privately Consumed Goods

The utility-maximizing choice of privately consumed goods for the representative

consumer is:

ci,t =

(1− τt)αiyt f or i ≤ It

αiyt f or i > It ,(2)

implying period indirect utility for privately-consumed goods equal to

v(yt ,τt ,bt) = γ + log(yt)+btlog(1− τt) , (3)

where γ ≡´ 1

0 αilog(αi)di is a constant. Ceteris paribus, utility from privately

consumed goods is increasing in the income endowment yt , decreasing in the tax

rate τt , and decreasing in the share of goods subject to tax bt .

The excess burden of taxation is the cost to the representative consumer of pay-

ing taxes on a narrow tax base relative to a world in which they remit the same tax

liability via a lump-sum tax. (In this model, a comprehensive tax base is equivalent

to a lump-sum tax, but is assumed here to be prohibitively expensive to adminis-

ter.) Measured in units of utility, the excess burden of taxation for a tax policy that

collects tax revenue R = τtbtyt is equal to:

EB(yt ,τt ,bt) ≡ v(yt −R,0,bt)− v(yt ,τt ,bt) (4)

= log(yt −R)− [log(yt)+btlog(1− τt)]

' log(yt −R)−[log(yt)−bt

(τt + τ2

t /2)],

11

where the approximate equality follows from taking a second-order Taylor series

approximation around τ = 0. In what follows, this excess burden of taxation will

sometimes be equivalently referred as deadweight loss or efficiency cost. Next,

consider the reduction in the excess burden of taxation due to a revenue-neutral

marginal increase in tax base breadth. This can be found by differentiation with

respect to bt , subject to the requirement that tax-revenue collected is unchanged.

The decline in excess burden is:

∂EB∂bt

=−log(1− τt)−τt

1− τt'−τ2

t2, (5)

with the approximation again due to a second-order Taylor series approximation

around τ = 0. The decline in excess burden due to a marginal increase in tax base

breadth is approximately proportional to the tax rate squared. As discussed in detail

later, this convexity plays a crucial role in explaining the occurrence of tax base

changes.7

2.4 Budget Constraint and Administrative Costs

Revenue raised by taxation of the privately consumed goods is used to fund provi-

sion of a public good. The government’s period budget constraint is given by

Gt = τtbtyt −ξ (yt ,bt−1,bt) , (6)

7The compensated elasticity of taxable income is equal to b, the expenditure share of taxed goods(see Slemrod and Kopczuk 2002, p. 108 ).

12

where Gt is spending on the public good and τtbtyt is revenue raised at rate τt , on

a tax base with breadth bt , and at income level yt . The administrative cost function

ξ (yt ,bt−1,bt) depends on both the current and previous period’s level of tax base

breadth, and the level of income:

ξ (yt ,bt−1,bt) = ξ f (bt)yt +ξF (bt−1,bt)yt , (7)

where ξ f (bt) is the per-period cost to administer a tax base with breadth bt , and

ξF (bt−1,bt) is a fixed cost incurred in undertaking a tax base broadening reform that

expands the expenditure share of commodities subject to tax from bt−1 to bt . For

simplicity, administrative cost is assumed to be linear in income: ξ (yt ,bt−1,bt) =

ξ (bt−1,bt)yt . This assumes away aspects of administrative cost that do not vary

proportionally with the value of the tax base, but does not change the model’s key

insights.8

The administrative cost required to collect tax revenue differs by commodity,

because it is more costly to verify and enforce tax liability for some commodities

than others. Commodities are assumed to be ordered in increasing administrative

cost, so that the per-period administrative cost function ξ f (bt) is monotonically in-

creasing and convex in tax base breadth. Reflecting the administrative infeasiblity

of making arbitrarily narrow distinctions between taxed and untaxed goods, the per-

period administrative cost function ξ f (bt) permits a finite number of levels of tax

base breadth. In practice, differentiating tax liability among highly substitutable

commodities is prohibitively expensive, because taxed purchases can be easily dis-

8Evasion and avoidance considerations suggest per-period administrative cost may be increasing inthe tax rate, but following Yitzhaki (1979) administrative cost is assumed to not be a function of thetax rate for tractability; this simplification does not affect the model’s key implications.

13

guised as untaxed purchases, and marginal changes in product specification could

be made to avoid tax liability. The per-period administrative cost function is shown

in Figure 1a. For ease of exposition, I show only a small number of feasible levels

of tax base breadth.

The fixed cost incurred when fiscal capacity is upgraded includes all one-time

expenses incurred by the tax administration required to collect revenue on a new

tax base, such as putting a reporting and compliance infrastructure in place (see

Slemrod and Yitzhaki 2002 on administrative costs). The infrequency with which

we observe fundamental changes in tax base breadth—such as the introduction, or

repeal, of a consumption tax—suggests that the fixed cost component to upgrade

fiscal capacity is large. I assume that there is no fixed cost associated with a tax

base narrowing reform.

2.5 Optimal Commodity Tax Rate and Indirect Utility

The government enters each period with tax base breadth bt−1 (determined in the

previous period), and knowing the current period’s income endowment yt . The

model assumes no frictions affecting the choice of the tax rate τt each period. Tak-

ing tax base breadth as given, the planner maximizes welfare for the representative

taxpayer (given by Equation 1), subject to the economy’s budget constraint (given

by Equation 6). The resulting first-order condition provides an implicit expression

(i.e., conditional on tax base breadth) for the optimal tax rate:

τ (yt ,bt−1,bt) =φ +ξ (bt−1,bt)

(bt +φ)+

Gyt (bt +φ)

. (8)

14

Holding administrative costs constant, a broader tax base requires a lower tax rate

to raise a given amount of revenue than a narrow tax base, and thus the optimum

tax rate is decreasing in tax base breadth.

Having solved for the optimal tax rate, I now state a regularity condition on the

slope of the administrative cost function, ensuring that a tax base expansion reduces

the tax rate, inclusive of the fixed cost to increase tax base breadth. This is a weak

assumption because the distortionary cost of taxation is proportional to the tax rate

squared, and thus a tax base broadening would never be optimal if the rate did not

fall. Assumption 1 below provides a formal statement, and summarizes the earlier

discussion on the convexity of the per-period administrative cost function.

Assumption 1: (The per-period administrative cost function is convex in tax-base

breadth; an increase in tax base breadth reduces the optimal tax rate) (a) ∆ξ f , j/∆b j

is increasing in tax base breadth b j, where ∆ξ f , j = ξ f(b j)−ξ f

(b j−1

)and ∆b j ≡

b j−b j−1 ; (b) administrative cost function is such that τ(yt ,b j,b j+1

)< τ

(yt ,b j,b j

),

for all j.

Next, making use of Equation (8), the implicit expression for the optimal tax

rate, define

v(yt ,bt−1,bt)≡ v(yt ,τ∗t ,bt)+φ log(G∗

t − G)

(9)

to be the utility for the representative taxpayer evaluated at the optimal tax rate,

where τ∗t = τ (yt ,bt−1,bt) and G∗t = τ∗t btyt −ξ (bt−1,bt)yt . This substitution simpli-

fies the analysis that follows by re-expressing welfare for the representative house-

hold in terms of only one choice variable for the planner each period: tax base

15

breadth bt . With some algebra, it can be shown that

v(yt ,bt−1,bt) = γ +φ logφ +(1+φ) logyt +(bt +φ) log(1− τ (yt ,bt−1,bt)) , (10)

where γ + φ logφ is a constant that does not depend on the tax rate or tax base

breadth. Reflecting concavity of utility for privately consumed goods and the public

good, the indirect utility function v(yt ,bt−1,bt) is strictly increasing and concave in

yt .

Lemma 1: (Utility is concave in income) v(y,b) is strictly concave in y.

Proof:

∂v∂y =

1+φy + b+φ

1−τ∂ (1−τ)

∂y > 0, using the fact that ∂ (1−τ)∂y = G

b+φ

(1y2

)≥ 0, and

∂ 2v∂y2 =−1+φ

y2 + b+φ1−τ

∂ 2(1−τ)∂y2 − b+φ

(1−τ)2

(∂ (1−τ)

∂y

)2< 0. !

2.6 Income Shocks and Tax Base Breadth

Evidence from U.S. state governments indicates that a sufficiently large fall in in-

come causes tax base expansion. For this to be optimal, the efficiency cost of a

narrow tax base must rise relative to a broad tax base when income falls. Efficiency

cost is approximately proportional to the tax rate squared (see Equation 4), and thus

the tax rate on a narrow base must rise by more than on a broad base when income

falls. The expression for the optimal tax rate, Equation (8), shows that if there is

no mandatory spending then the tax rate does not vary with income: demand for

private and public consumption varies proportionally. But with a positive level of

mandatory spending, revenue needs vary less-than-proportionally with income, and

the tax rate rises when income falls. The tax rate rises by more with a narrow than

a broad tax base, and thus the efficiency cost of a narrow tax base rises relative to a

16

broad tax base. Formally, per-period utility rises with a broad tax base (inclusive of

the fixed administrative cost) relative to a narrow tax base when income falls if

∂v(yt ,b j,b j+1)

∂y−

∂v(yt ,b j,b j)

∂y=

Gy2

[1

1− τ (yt ,b j,b j+1)− 1

1− τ (yt ,b j,b j)

]< 0 (11)

for all j, where b j+1 > b j. I assume that U.S. state governments had a mandatory

level of spending G> 0, ensuring that a fall in income raises the value of a broad tax

base relative to a narrow tax base. Validating this assumption, government spending

rose as a share of income in the Great Depression, and states experiencing above-

average negative income shocks were the most likely to adopt a retail sales tax.

Assumption 2, and its Corollary summarizes this discussion.

Assumption 2: There is a positive level of mandatory spending: G > 0.

Corollary: (A fall in income raises per-period utility with a broad tax base rel-

ative to a narrow tax base, the more so the larger is mandatory spending) As-

sumption 2 implies: i) ∂[v(yt ,b j,b j+1

)− v

(yt ,b j,b j

)]/∂y is negative; and ii)

∂ 2 [v(yt ,b j,b j+1

)− v

(yt ,b j,b j

)]/∂y∂G is negative.

Proof: By Assumption 1, τ(yt ,b j,b j+1

)< τ

(yt ,b j,b j

), and by Assumption 2 G >

0. i) follows from (11), and ii) follows from differentiation of (11). !

Figure 1b shows indirect utility as a function of income, for different levels of

tax base breadth. Utility is strictly concave in income for each level of tax base

breadth, but the degree of curvature is greater at lower levels of tax base breadth

(Lemma 1; Assumption 2 and its Corollary). As income falls, the degree of cur-

vature becomes sufficiently great at low levels of tax base breadth that the curves

intersect; Lemma 2 provides a formal statement. For the set of indirect utility func-

17

tions shown in Figure 1b, utility is highest at tax base breadth b1 for income levels

yt > y2. At lower levels of income yt ∈ (y3,y2), utility is greatest at the higher level

of tax base breadth b2. Similarly for the other levels of tax base breadth shown.

The solid line (the upper envelope) shows the maximum level of per-period utility

at each level of income.

Lemma 2: (For a sufficiently large fall in income, per-period utility is higher with

a broad than a narrow tax base, inclusive of the fixed administrative cost) Sup-

pose v(y,b j,b j

)> v

(y,b j+1,b j+1

), then there exists y < y such that v

(y,b j,b j

)<

v(y,b j,b j+1

)< v

(y,b j+1,b j+1

). Furthermore, v

(y,b j,b j

)intersects v

(y,b j,b j+1

)

and v(y,b j+1,b j+1

)only once.

Proof: Define f j (y) ≡ v(y,b j,b j+1

)− v

(y,b j,b j

). Then, note f j (y) < 0, because

v(y,b j+1,b j+1

)> v

(y,b j,b j+1

)and by assumption v

(y,b j,b j

)> v

(y,b j+1,b j+1

).

Next, define y j ≡ G/(b j −ξ

(b j,b j

)). Assumption 1b implies limy→y jτ

(y,b j,b j

)=

1 and limy→y jτ(y,b j,b j+1

)< 1. Hence, limy→y j f j (y) = ∞. The function f j is con-

tinuous in y, and thus by the Intermediate Value Theorem, there exists y j < y < y

such that f j (y)= 0. The Corollary implies that ∂ f j (y)/∂y< 0, and thus v(y,b j,b j

)

and v(y,b j,b j+1

)intersect at most once. Because v

(y,b j+1,b j+1

)> v

(y,b j,b j+1

)

for all y, it is also the case that v(y,b j,b j

)< v

(y,b j+1,b j+1

)and v

(y,b j,b j

)inter-

sects v(y,b j+1,b j+1

)once. !

2.7 Optimal Tax Base Breadth

The existence of a fixed cost to expand tax base breadth makes the optimal choice

of tax base breadth a dynamic optimization problem. The government enters period

t knowing the income level yt and carrying over tax base breadth bt−1 from the

18

previous period; it chooses bt to maximize the expected discounted lifetime utility

for the representative taxpayer:

V (yt ,bt−1) = maxbt

{v(yt ,bt−1,bt)+βEyV (yt+1,bt)

}, (12)

where β is the government’s rate of time preference. In what follows, I simplify the

analysis by restricting attention to two levels of tax base breadth: bL(ow) and bH(igh).

This is reasonable for this application because, although there were differences in

breadth of the retail sales tax bases adopted by U.S. state governments, the main

distinction is between states that did and did not adopt a retail sales tax. Equation

(12) implies that it is optimal to undertake a tax base broadening reform if

v(yt ,bL,bH)− v(yt ,bL,bL)> βEy [V (yt+1,bL)−V (yt+1,bH)] , (13)

and to undertake a tax base narrowing reform if

βEy [V (yt+1,bL)−V (yt+1,bH)]> v(yt ,bH ,bH)− v(yt ,bH ,bL) . (14)

The left-hand-side of (13) rises as income falls (see the Corollary to Assumption 2),

and the right-hand-side of (13) does not vary with current income, because income

shocks are assumed to be iid. This implies that for a sufficiently large fall in income,

the per-period efficiency cost of a narrow tax base is sufficiently high that (13) is

satisfied, and a tax base broadening reform is optimal. Once incurred, the fixed

cost required to expand tax base breadth creates option value, because a tax base

narrowing reform can be undertaken each period at no cost; this is stated formally

19

below in Lemma 3. When the option value of maintaining a broad tax base is large,

it can be optimal to maintain a broad base at normal income levels, even if it is not

optimal to undertake a tax base broadening reform at normal income levels. The

inaction region within which it is optimal to maintain a narrow or a broad tax base

is characterized by income levels for which neither (13) or (14) is satisfied:

v(yt ,bH ,bH)− v(yt ,bH ,bL) > βEy [V (yt+1,bL)−V (yt+1,bH)]

> v(yt ,bL,bH)− v(yt ,bL,bL) . (15)

The width of the inaction region is increasing in the size of the fixed cost to expand

tax base breadth. For a tax base narrowing reform to be optimal, income must be

sufficiently high that (14) is satisfied. When income rises, the per-period benefit of

a broad tax base relative a narrow tax base, given by the right-hand-side of (14),

falls, but the option value of maintaining a broad tax base, given by the left-hand-

side of (14), does not vary with current income. If the right-hand-side of (14) falls

sufficiently far, it is optimal to undertake a tax base narrowing reform.

The Proposition below summarizes this discussion, and is the key implication

of the model that I test empirically. In particular, I test whether there is an income

threshold below which a government with a narrow tax base undertakes a tax base

broadening reform. When income returns to normal levels, the Proposition states

that a government may either retain a broad tax base, or undertake a tax base nar-

rowing reform.

Lemma 3: (There is option value to maintaining a broad tax base) EyV (y,bH) >

EyV (y,bL).

20

Proof: A tax base narrowing reform can be undertaken each period at no cost,

implying V (y,bH) ≥ V (y,bL). Lemma 2 implies that for sufficiently low income

realizations per-period utility is higher with a broad than a narrow tax base. Thus,

EyV (y,bH)> EyV (y,bL). !

Proposition: (Optimal choice of tax base breadth) Assume that an initially nar-

row tax base breadth is optimal at mean income: v(y,bL,bL)+βEyV (yt+1,bL) >

v(y,bL,bH)+βEyV (yt+1,bH). Then: (i) there exists an income level yH < y such

that for y < yH it is optimal to undertake a tax base broadening reform; (ii) if the

fixed administrative cost is not too large, then there exists an income level yL > yH

above which a tax base narrowing reform is optimal; (iii) there is an inaction re-

gion within which it is optimal to maintain either a high or low tax base breadth:

if yL exists then the inaction region is yH < y < yL, otherwise it is never optimal to

undertake a tax base narrowing reform and the inaction region is y > yH.

Proof: Lemma 3 and iid income shocks implies that Ey [V (y,bL)−V (y,bH)] is

strictly negative and does not depend on current income. The remainder of the

proof proceeds in three parts: (i) Assumption 2 implies that the left-hand-side of

(13) is strictly decreasing in income, and Lemma 2 implies that for sufficiently

low income levels v(yt ,bL,bH) > v(yt ,bL,bL). Thus, there exists yH that satis-

fies (13) with equality, and y < yH for which a tax base broadening reform is op-

timal. (ii) If ξF (bL,bH) is sufficiently small, then there exists yH above which

it is optimal to undertake a tax base narrowing reform. A sufficient condition is

limy→∞

[v(y,bH ,bH)− v(y,bH ,bL)] < v(y,bL,bH)− v(y,bL,bL).This condition can be

derived by noting that βEy [V (yt+1,bL)−V (yt+1,bH)]> v(y,bL,bH)−v(y,bL,bL)

given that an initially narrow tax base is assumed to be optimal, and then using

21

(14). (iii) The right-hand-side of (14) is strictly greater than the left-hand-side of

(13), and Assumption 2 implies that both terms are decreasing in income. Thus,

yL > yH and there exists an inaction region: yH < y < yL, or y > yL. !

In the next section, I first show that the behavior of U.S. state governments dur-

ing the Great Depression supports the Proposition. I then show that the relationship

between income shocks and retail sales tax base adoption predicted by the model is

robust to a variety of controls.

3 Empirical Analysis

3.1 Background

This behavior of U.S. state governments during the Great Depression provides an

excellent opportunity to examine whether an economic slump causes tax base ex-

pansion. As mentioned in the introduction, the U.S. Great Depression was deep

and prolonged. Per capita U.S. real GDP fell by 29 percent peak-to-trough, and

took a decade to regain its 1929 level. There was also substantial heterogeneity

in the size of income shocks experienced across states. Virginia experienced a fall

in real per capita income of “only” 12 percent between 1929 and 1933, while at

the other extreme South Dakota suffered a 56 percent collapse in income over the

same period. Garrett and Wheelock (2006) show that the size of income shocks

experienced by states is correlated with industrial structure, but not the level of

government spending or pre-Depression income levels. Both the time series and

cross-sectional variation in income is useful for identifying the effect of income

shocks on tax base breadth.

22

U.S. state government total revenue as a share of income was relatively small

prior to the Great Depression, averaging 3.3 percent in 1927. These revenues were

collected from a narrow set of tax bases. In 1932, by which point only two states

had introduced a retail sales tax, state governments on average raised 60 percent of

their tax revenue from license and permit taxes, 27 percent from general property

taxes, 5 percent from inheritance taxes, and the remaining 8 percent from a range of

less prominent taxes. While none of the U.S. states had a retail sales tax prior to the

Great Depression, 12 states levied an individual income tax, and 10 had a corporate

net income tax (see Table 1). Most states levying a corporate net income tax did so

to prevent revenue leakage from their personal income tax base.

Because there is no borrowing or lending in the model, a comprehensive income

and retail sales tax base are theoretically equivalent; for a state with a comprehen-

sive income tax, the addition of a retail sales tax would not represent a tax base ex-

pansion. In practice, personal income tax bases were narrow, and the introduction

of retail sales tax bases represented a substantial increase in tax base breadth. Per-

sonal income taxes were owed mainly by very high income earners, who were taxed

at low rates (Bakija, 2009). Withholding at source for personal income taxes did

not begin to be introduced at the state government level until 1948 (Dušek 2006),

limiting the ability of state income taxes to reach a large share of the population.

3.2 Tax Base Adoption During the Great Depression

The Great Depression had a profound impact on U.S. state government tax struc-

ture. None of the U.S. states had a broad-based consumption tax in 1929, but by

the 1933 trough in U.S. real GDP, 11 state governments levied a retail sales tax. By

23

1938, at which point U.S. per capita real GDP was still below its 1929 level, 28

states had levied a retail sales tax for at least one year. All but six of the 28 new

retail sales taxes introduced during the 1930s have been levied continuously until

the present day (see Table 1 and Figure 2). Retail sales tax rates were low compared

to present levels, with states imposing either a 2 or 3 percent rate in the 1930s (Due

and Mikesell, 1995).

In the cross-sectional dimension, governments in states experiencing larger-

than-average falls in income were significantly more likely to introduce a retail

sales tax than those experiencing smaller-than-average income shocks. Figure 3

shows this by plotting average per capital real income for states that did and did not

introduce a retail sales tax during the 1930s. States introducing a retail sales tax

experienced a 7 percent larger fall in real per capita income on average than those

not levying a retail sales tax, and the recovery in incomes was slower.

The first panel in Table 2 provides an alternate way to see the relationship be-

tween income shocks and retail sales tax base adoption, grouping states by the fall in

real per capita income experienced between 1929 and 1933 and reporting the share

of states in each income growth category introducing a retail sales tax. A clear

monotonic relationship is evident: a retail sales tax was introduced by 30 percent

of states experiencing a less than 20 percent fall in income, by 50 percent of states

experiencing a 20-30 percent fall in income, by 70 percent of states experiencing

a 30-40 percent fall in income, and by all four states experiencing a larger-than 40

percent fall in income.

Regression analysis confirms the relationship between income shocks and retail

sales tax base adoption evident in the first panel of Table 1. The dependent vari-

24

able for Regression (1) in Table 6 is an indicator taking the value unity if a state

introduced a retail sales tax in the 1930s. Each 10 percent fall in real per capita

income between 1929 and 1933 is estimated to have increased the probability that

a state government introduced a retail sales tax by 0.16. The regression controls for

existing tax structure (the presence of personal and corporate income taxes), pre-

Depression debt levels, and fiscal institutions, each of which is discussed in more

detail later. Regression (2) estimates the same relationship as Regression (1) using a

probit model rather than a linear probability model. A similarly strong relationship

between income shocks and retail sales tax base adoption is evident. Restricting

attention to states whose retail sales tax ultimately became permanent has little im-

pact on the estimated relationship between income shocks and tax base adoption

(see Regression 3 in Table 6 and the first panel in Table 2).

The introduction of retail sales tax bases during the 1930s was accompanied by

the adoption of additional individual income tax bases. A further 16 states intro-

duced an individual income tax during the 1930s, of which 14 ultimately became

permanent (see Table 1). Table 3 shows combinations of retail sales and individual

income tax bases introduced during the 1930s. Most states introducing a retail sales

tax base either had an individual income tax base prior to the Great Depression or

introduced one together with an income tax. Only four states introduced an indi-

vidual income tax but not a retail sales tax. This indicates that income taxes were

in general a complement rather than a substitute to retail sales tax bases.

Regression (4) in Table 6 tests whether the size of income shock experienced

by a state increased its propensity to adopt an individual income tax base. The

dependent variable is an indicator variable taking the value unity if a state govern-

25

ment introduced an individual income tax base during the 1930s, and the sample is

restricted to states that did not have an individual income tax base in 1929. Control-

ling for retail sales tax base adoption, the coefficient on the income shock variable

is small and insignificant. Income tax bases were a less important source of revenue

than retail sales tax bases, and were introduced in part to reduce the perceived re-

gressivity of retail sales tax bases (Penniman, 1980; Due and Mikesell, 1995).9 For

these reasons, I focus mainly on the adoption of retail sales tax bases.

3.3 Spending and Revenues

In the model, a sufficiently deep economic slump causes tax base expansion because

government spending varies less-than-proportionally with income (Assumption 2).

Consistent with this, the lower panel in Figure 4a shows that spending rose sharply

as a share of income between 1927 and 1932. (Consistent revenue and spending

data are available at 5-year intervals from the Census of Governments.) By 1937,

average state income had recovered most of its 1929 level, and spending fell as a

share of income. However, government spending as a share of income remained

above its level prior to the Great Depression. This reflects a long-run trend in gov-

ernment spending, which can be seen in the top panel of Figure 4a.

The introduction of retail sales tax bases in the 1930s did not happen because

some states increased spending relative to others, and so had greater revenue needs.

Regression (5) shows no significant relationship between the change in real per

9By 1942, the 22 states that had adopted a retail sales tax during the 1930s raised on average 19percent of their total tax revenue from the sales tax, compared to an 11 percent income tax revenueshare for the 35 states collecting income tax revenue in 1942. Note that income tax revenue-sharedata include inheritance taxes.

26

capita state government spending over the period 1932 to 1937 and the propensity

of state governments to adopt a retail sales tax.10 Over the period 1927 to 1952,

average spending was similar for states that did and did not introduce a retail sales

tax (see the top panel of Figure 4a). Over the 1932 to 1937 period, when almost all

of the retail sales tax bases were introduced, spending growth was slower than over

the earlier 1927 to 1932 period, or subsequent periods. State government tax bases

were stressed during the Great Depression by a fall in incomes rather than a rise in

spending.

Reflecting the limited ability of state governments to borrow, revenues and

spending were closely matched (see the upper panels of Figures 4a and 4b). Be-

cause government spending rose as a share of income in the Great Depression, so

did revenues (see the lower panel of Figure 4b). But Regression (5) shows no statis-

tically significant relationship between retail sales tax base adoption and growth in

real per capita total revenues or tax revenues between 1932 and 1937. This implies

that, consistent with the model, governments introducing a retail sales tax base were

able to raise revenue at lower tax rates, and thus less distortionary cost, than states

that did not introduce a retail sales tax.

3.4 Property Tax

The model assumes that a decline in income causes a proportional reduction in tax

base value. For most tax bases this is untestable. While data on revenue collections

by tax base are available, data on average tax rates and taxable value are not. An

10The dependent variable in Regression (5) excludes temporary retail sales tax bases because all sixhad been repealed by 1937.

27

exception is the property tax base, for which data on assessed property values are

available. The property tax base was the second most important source of revenue

for state governments. On average, general property taxes comprised 26 percent of

total state government tax revenue in 1932.

State governments are likely to have been particularly unwilling to raise prop-

erty tax rates during the Great Depression to fund revenue shortfalls, for fear of

forcing property owners into foreclosure. This is a concrete example of a situa-

tion in which the marginal efficiency cost of funds is sharply increasing in the tax

rate. Thus, large declines in property values created strong incentives for state gov-

ernments to introduce a retail sales tax. Figure 5 sorts states by their percentage

change in assessed real property tax values over the period 1929 to 1937. A longer

period than the 1929 to 1933 peak-to-trough in incomes is used because changes

in assessed property values typically lag changes in the market value of property.11

Although delayed, the peak-to-trough (1929-1933) fall in incomes was reflected on

average about one-for-one in lower assessed property values by 1937. A clear re-

lationship is evident between declines in assessed property values and retail sales

tax base adoption: 17 of the 27 states experiencing a fall in assessed real property

values between 1929 and 1937 had a retail sales tax in 1937, whereas only 2 of the

16 states experiencing a rise in property values had a retail sales tax in 1937. (States

without a property tax in 1929 are excluded. See the notes to Figure 5.)

11Comprehensive data on assessed property values are unavailable between 1932 and 1937.

28

3.5 The Role of Debt

The model assumes away debt, with governments constrained to balance revenues

and expenditures period-by-period. Justifying this assumption, debt issue did not

play a meaningful role smoothing fluctuations in income during the Great Depres-

sion. For most states, there were constitutional or procedural barriers to debt is-

sue that prevented governments from running temporary deficits. At the onset of

the Great Depression, a constitutional amendment was required to issue debt in 18

states, and a statewide referendum was required in 15 other states (Ratchford, 1938).

Among the remaining 15 states for which the effective power to issue debt resided

state legislatures, balanced budget requirements for operating expenses were in

force in 7 states (Ratchford, 1938; Rodriguez-Tejedo, 2007).12 The first state gov-

ernment rainy-day fund did not come into existence until 1945 (Rodriguez-Tejedo,

2007).

Largely reflecting differences in capital works programs, state governments en-

tered the Great Depression with varying levels of debt. Overall, state government

debt-to-revenue ratios were moderate in 1929 compared to earlier years (see Table

4). The top panel in Figure 6 shows that, except for Arkansas and South Carolina,

there was little change in nominal debt outstanding during the Great Depression.13

But because debt was largely fixed in nominal terms, the 24 percent peak-to-trough

fall in the price level, measured by the U.S. GDP deflator, raised the real value of

debt (see the lower panel of Figure 6). This led to a wave of credit rating down-

12During the 1930s a few states adopted more stringent fiscal institutions: Alabama introduced aconstitutional balanced budget requirement in 1933, as did New York in 1938. Arkansas removedthe effective power to issue debt from legislators in 1934, and put it in the hands over voters viareferendum, with North Carolina following suit in 1936 (Ratchford, 1938).

13Arkansas assumed local government debts during the Great Depression (Ratchford, 1941).

29

grades: 45 states had a Aaa credit rating in 1929, 35 in 1932, and 13 in 1937 (see

Table 5). But only one state, Arkansas, defaulted on any of its debt obligations.14

Regression (1) in Table 6 indicates that state governments entering the Great

Depression with high debt-to-income ratios were more likely to adopt a retail sales

tax than those with low debt-to-income ratios. Each one percentage point increase

in the 1929 debt-to-income ratio is estimated to have increased the probability that

a state government introduced a retail sales tax by about 0.05; the estimated mag-

nitude is similar across regression specifications. But the association between pre-

Depression debt levels and tax base adoption appears to largely be driven by the be-

havior of a few highly indebted states. The lower panel of Figure 2 shows that 4 of

the 5 most highly indebted states in 1929 adopted a retail sales tax during the Great

Depression, but indicates no clear association among the other states. Regression

(6) confirms this: excluding the five states with the highest 1929 debt-to-income

ratios, there is little evidence of a relationship between debt levels and retail sales

tax base adoption.

For the five most highly indebted states, interest expense became a large share

of spending during the Great Depression, averaging 14.6 percent of total spend-

ing in 1932. In the model, interest expense is an example of mandatory spending:

with non-state-contingent debt, scheduled interest payments do not vary with in-

come. The larger the level of mandatory spending, the greater is the benefit of a

tax base broadening reform when income declines, as formalized in the Corollary

to Assumption 2. This provides the most likely explanation for the correlation be-

14In August 1932 Arkansas defaulted on some district bonds, and by March 1933 had defaulted onall its highway debt. By 1937 almost all highway debt had been refunded into new bonds shiftingthe repayment burden out to a 40-year horizon, with no new debt maturing before 1943-44. SeeRatchford (1941) for a more detailed account.

30

tween pre-Depression debt levels and retail sales tax base adoption. There is little

evidence that states entering the Great Depression with high debt levels introduced

retail sales tax bases because they had less ability than low-debt states to buffer

income shocks through borrowing.

There is some evidence that receiving a credit rating downgrade made state gov-

ernments more likely to adopt a retail sales tax, conditional on income shocks and

debt levels. But the evidence is not strong. Regression (7) augments the baseline

specification, Regression (1), with state government debt credit ratings in 1937, by

which point ratings had reached their minimum for most states. Relative to Aaa-

rated states, Aa-rated states were more likely to introduce a retail sales tax, but the

null that credit ratings had no influence on retail sales tax base adoption cannot be

rejected for states experiencing larger rating downgrades.

3.6 Cross-State Heterogeneity

This section briefly considers remaining sources of heterogeneity among the states

that could have affected incentives to adopt a retail sales tax.

Initial Tax Structure

As discussed earlier, the most prominent source of tax revenue for state govern-

ments in 1932 (prior to the introduction of all but two retail sales tax bases) was

license and permit income, followed by general property taxes. Figure 7 shows that

initial tax structure was similar for states that did and did not introduce a retail sales

tax during the 1930s. Sales-tax-adopting states relied a little more heavily on prop-

erty taxes and a little less on license and permit income than non-adopting states,

31

but these differences are small compared to the relative importance of the different

tax bases.

Fiscal Institutions

Differences in fiscal institutions do not appear to have been an important factor

influencing retail sales tax base adoption. The coefficient on the Constitution vari-

able in Regression (1) is not statistically different than zero, indicating that state

governments requiring a constitutional amendment to issue debt were not signif-

icantly more likely to introduce a retail sales tax than those for which the effec-

tive power to issue debt resided in the legislature, conditional on other variables.

However, state governments requiring a referendum to issue debt are estimated to

have been more likely to introduce a retail sales tax. A statewide referendum is

arguably no more difficult to pass than a constitutional amendment, so this differ-

ence is unlikely to be economically meaningful. Regression (8) shows that there is

no relationship between tax base adoption and the presence of a balanced budget

requirement.15

Alcohol Sales Taxes

Following the repeal of Prohibition in 1933, all states introduced alcoholic bev-

erage taxes. There was no strong tendency for states without a retail sales tax to

rely more heavily on alcoholic beverage taxes: the 22 states with a retail sales tax

in 1942 collected on average 4 percent of total tax revenues from alcohol taxes, only

a little less than the 6 percent share for states without a retail sales tax.15Thanks to Isabel Rodriguez-Tejedo for sharing data on state government balanced budget require-

ments.

32

4 Discussion

The behavior of U.S. state governments during the Great Depression provides strong

support for the model. The collapse in economic output during the Great Depres-

sion caused a wave of retail sales tax base adoption, with states experiencing the

largest falls in income being the most likely to introduce a retail sales tax. The only

source of heterogeneity between states in the model is the size of income shocks

experienced, and so there is a threshold income level below which all states are pre-

dicted to undertake a tax base broadening reform. In reality, there are other sources

of heterogeneity between states, and there is no threshold income level below which

all states introduced a retail sales tax, and above which none did. But there do not

appear to be any sources of heterogeneity between the states that would provide an

alternative explanation for the relationship between income shocks and retail sales

tax base adoption. Among states that did and did not adopt a retail sales tax dur-

ing the 1930s, average spending levels and spending growth were similar, as was

initial tax structure. Differences in fiscal institutions do not appear to have been

an important factor influencing tax base adoption. State governments entering the

Great Depression with high debt levels were more likely to introduce a retail sales

tax than those with low debt levels, but this can be easily understood in terms of the

model. Interest expense did not fall with incomes during the Great Depression, and

so comprised a large share of spending for states entering the Great Depression with

high debt levels. This stressed initially narrow tax bases, and made the introduction

of a retail sales tax desirable.

In the model, the larger is the fixed cost to expand tax base breadth, the greater

is the option value to maintaining a broad tax base once incomes have recovered.

33

And the smaller is the per period administrative cost, the more likely is a broad tax

to be optimal once the fixed cost has been incurred. Of the 28 retail sales tax bases

introduced during the Great Depression, all but six have remained in place contin-

uously until the present day. This suggests that the fixed cost is large relative to the

incremental per period administrative cost to maintain a broad tax base. But this

conclusion is necessarily more tentative than evidence on the relationship between

income shocks and retail sales tax base introduction. The permanence of retail sales

tax bases could reflect a range of factors beyond the scope of the model that have

influenced tax base breadth over subsequent decades. For example, the Peacock

and Wiseman (1961) displacement hypothesis predicts changes in fiscal capacity to

proceed in a steplike manner because each improvement in fiscal capacity increases

society’s tolerance for new revenue-raising methods.

The 1930s wave of tax base adoption was the largest, but U.S. state governments

continued to introduce retail sales and income tax bases in subsequent decades (see

Table 1). The 1960s was the next most important decade, with twelve states intro-

ducing a retail sales tax and seven an individual income tax. Increased social and

education spending was a key factor influencing tax base expansion in the 1960s

(Due and Mikesell, 1995). Such changes in demand for public spending are be-

yond the scope of the model, but the distortionary cost of taxation emphasized by

the model remains relevant. A large increase in government spending funded by

narrow tax bases requires high tax rates, which raises the deadweight cost of taxa-

tion. A sufficiently large increase in spending makes a tax base broadening reform

optimal. But because the level of public good provision is endogenous to tax base

breadth — a broader tax base lowers the deadweight cost of taxation and makes a

34

higher level of spending optimal — causality from spending to tax base adoption

is unclear in the 1960s. This is in contrast to the Great Depression, which provides

plausibly exogenous variation in fiscal stress.

5 Conclusion

This paper contributes to the literature on state fiscal capacity by providing a new

explanation for tax base broadening reforms. It shows, theoretically and empiri-

cally, that an economic slump can be an important stimulant to investment in fiscal

capacity. This complements the existing literature, which has emphasized political-

economy explanations for the adoption of broad-based income and consumption

taxes in developed economies.

In the model, tax collections fall in an economic slump, but demand for public

spending falls by less. This puts stress on the revenue raising capability of narrow

tax bases, particularly when the ability to borrow is limited. Raising the tax rate

on narrow tax bases increases revenue collections, but raises the deadweight cost of

taxation, which is convex in the tax rate. For a sufficiently deep economic slump,

it is optimal to incur the fixed cost necessary to expand tax base breadth. Doing so

enables revenue to be raised by taxing a wider range of economic activity at a lower

rate, and thus in a less distortionary manner. Even though macroeconomic income

shocks are transitory, improvement in fiscal capacity can be long-lasting. The fixed

cost to upgrade fiscal capacity is sunk, and it can be optimal to maintain a high level

of fiscal capacity even after incomes have recovered.

Evidence from the behavior of U.S. state governments during the Great Depres-

35

sion provides robust support for the model. At the onset of the Great Depression,

none of the U.S. state governments levied a retail sales tax, but by 1938 22 state

governments had adopted a retail sales tax that ultimately became permanent, and a

further six states had levied a temporary retail sales tax. The cross-sectional pattern

of tax base adoption also provides strong support for the model. Governments in

states experiencing larger than average negative income shocks were significantly

more likely to adopt a retail sales tax than were governments in states experiencing

smaller than average income shocks.

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, American State Debts, Durham NC: Duke University Press, 1941.

Rodriguez-Tejedo, Isabel, “State Fiscal Institutions.” PhD dissertation, University

37

of Maryland 2007.

Slemrod, Joel and Shlomo Yitzhaki, “Tax Avoidance, Evasion, and Administra-tion,” in Alan J. Auerbach and Martin Feldstein, eds., Handbook of Public Eco-nomics, Vol. 3, Elsevier, 2002, chapter 22, pp. 1423–1470.

and Wojciech Kopczuk, “The Optimal Elasticity of Taxable Income,” Journalof Public Economics, April 2002, 84 (1), 91–112.

Tilly, Charles, “Reflections on the History of European State-Making,” in CharlesTilly, ed., The Formation of Nation States in Western Europe, Princeton NJ:Princeton University Press, 1975.

U.S. Department of Commerce, Statistical Abstract of the United States, Wash-ington DC: United States Government Printing Office, Bureau of Foreign andDomestic Commerce, Various Years.

U.S. Department of Commerce: Bureau of Economic Analysis, “Regional Eco-nomic Accounts: State Personal Income,” Available at: bea.gov/regional.

Wilson, John D., “On the Optimal Tax Base for Commodity Taxation,” AmericanEconomic Review, December 1989, 79 (5), 1196–1206.

Yitzhaki, Shlomo, “A Note on Optimal Taxation and Administrative Costs,” Amer-ican Economic Review, June 1979, 69 (3), 475–480.

38

Table 1: Number of U.S. States with Tax Base: By DecadeRetail Sales Individual Income Corporate Income

Permanent Temporary Permanent Temporary Permanent Temporary Total1900-09 0 0 0 0 0 0 01910-19 0 0 8 0 4 0 121920-29 0 0 12 0 10 0 221930-39 22 6 28 2 24 1 831940-49 27 0 28 2 25 1 831950-59 32 0 28 0 28 0 881960-69 44 0 35 0 33 1 1131970-79 44 0 39 0 34 1 118

Notes: Alaska and Hawaii, which achieved statehood in 1959, are excluded. Narrow individual in-come tax bases are also excluded: New Hampshire and Tennessee have bases taxing only interest anddividend income, and Connecticut a base that taxes only capital gains and dividends. Temporary retailsales taxes in the mid-1930s in Idaho, Kentucky, Maryland, New Jersey, New York and Pennsylvaniawere in place for only one or two years in each state. Louisiana is classified as permanently introduc-ing the retail sales tax in 1938 because its 1940 repeal lasted only one year. South Dakota and WestVirginia had an individual income tax from the 1930s until 1942, and South Dakota had a corporatenet-income tax from 1935-1943. Michigan had a corporate net-income tax from 1967-1975. Sources:State retail sales tax data are from Due and Mikesell (1995) and income tax data are from Penniman(1980).

Table 2: Upgrading of Fiscal Capacity: Bivariate AnalysisAverage Interest Sales TaxExpense Ratio Number Share: 1930s

1932 of States All PermanentIncome Shock: 1929-33 < 20 8 0.3 0.1

20-30 21 0.5 0.330-40 15 0.7 0.740-50 3 1.0 1.0> 50 1 1.0 1.0

Debt/Income: 1929 < 0.01 1.1 8 0.3 0.30.01-0.02 2.7 16 0.7 0.40.02-0.03 3.6 9 0.7 0.40.03-0.06 7.6 10 0.5 0.5

> 0.06 14.6 5 0.8 0.8Notes: Income Shock: 1929-33 is the percentage decline in real state per capita personalincome from 1929-1933. Interest Expense Ratio 1932 is interest expense as a share oftotal spending. Sales Tax Share: All is the fraction of states in each category that levied aretail sales tax in the 1930s, and Sales Tax Share: Permanent is the fraction that introduceda retail sales tax in the 1930s that ultimately became permanent. Sources: BEA, Due andMikesell (1995), Penniman (1980), and U.S. Department of Commerce.

39

Table 3: Combinations of Tax Bases Introduced in 1930s:Number of States

Individual Income TaxYes: Existing Yes: New No Total

Retail Sales Yes 7 14 7 28Tax Introduced No 5 4 11 20

Total 12 18 18Notes: Individual Income Tax: Yes: Existing are states that had an individual in-come tax in 1929, Yes: New are states that introduced an individual income tax inthe 1930s, and No are states that did not have an individual income tax in 1929 or in-troduce one in the 1930s. Retail Sales Tax Introduced: Yes are states that introduceda retail sales tax in the 1930s, and No those that did not. Before 1930 no state gov-ernments had a retail sales tax. Totals include 6 temporary retail sales tax bases and2 temporary individual income tax bases. 14/15 states that introduced a corporateincome tax during the 1930s did so together with an individual income tax. Source:Due and Mikesell (1995); Penniman (1980).

Table 4: Debt-to-Revenue Ratios: Number of U.S. States1890 1902 1912 1922 1927 1929 1932 1937 1942 1947 1952

0.0-0.5 11 15 22 18 19 20 19 23 29 36 320.5-1.0 6 14 6 14 13 15 13 12 12 11 111.0-3.0 15 12 18 16 15 11 12 12 7 1 5> 3.0 13 7 2 0 1 2 4 1 0 0 0

Average 2.62 1.47 0.91 0.80 0.87 0.93 1.09 0.66 0.52 0.27 0.44Median 1.59 0.83 0.54 0.71 0.71 0.67 0.63 0.51 0.39 0.17 0.30

Federal Govt. 2.78 2.10 1.72 5.70 4.61 4.38 10.13 6.76 4.95 6.71 3.92Notes: Debt is par value of gross debt less sinking fund assets. Revenue data for 1902 and 1912 areunavailable, and data for 1903 and 1913 has been used instead. Data for three states are missing for 1890.Average values are unweighted. Source: U.S. Department of Commerce (Various Years).

Table 5: Moody’s General Obligation Bond RatingsNumber of U.S. States by Rating Category

1922 1927 1929 1932 1937 1942 1947 1952Aaa 48 44 45 35 13 15 24 22Aa 0 2 2 10 15 18 16 13A 0 0 0 2 11 12 7 9

Baa 0 0 0 0 5 2 0 0Ba 0 0 0 0 1 0 0 0

Unrated 0 2 1 1 3 1 1 4Notes: Where a state is unrated for the year noted, the state is assignedits rating for the subsequent year. If a rating is unavailable, states witha debt-to-revenue ratio of no more than 0.1 were assigned a Aaa rating.Unrated states noted in the table fall into neither of these categories. Thenumber of assigned ratings for the years shown 1922-1952, respectively,is 2, 0, 3, 3, 6, 7, 11, and 9. According to Moody’s, the absence of arating provides no indication of the credit worthiness of an issuer. Source:Moody’s Municipal and Government Manual (1920-1950) .

40

Table 6: Upgrading of Fiscal Capacity: Cross-State Regression Analysis(1) (2) (3) (4) (5) (6) (7) (8)

Sales Tax Sales Tax Sales Tax Income Tax Sales Tax Sales Tax Sales Tax Sales Tax1930s 1930s Permanent 1940 Permanent 1930s 1930s 1930s

ex-High DebtOLS Probit OLS OLS OLS OLS OLS OLS

Income Tax 1929 0.141 0.142 0.066 0.030 0.129 0.210* 0.100(0.137) (0.181) (0.163) (0.157) (0.162) (0.119) (0.198)

Corporate Tax 1929 -0.241 -0.337 -0.089 -0.009 -0.171 -0.246* -0.306(0.164) (0.208) (0.162) (0.155) (0.183) (0.129) (0.197)

Sales Tax 1930s 0.320(0.193)

ΔInc. 1929-33 -0.016*** -0.024*** -0.018*** -0.006 -0.017*** -0.016*** -0.016*** -0.016***(0.004) (0.007) (0.004) (0.005) (0.003) (0.004) (0.005) (0.005)

Debt: 1929 0.050*** 0.073*** 0.056*** 0.081** 0.049*** 0.023 0.040** 0.042***(0.014) (0.024) (0.014) (0.032) (0.011) (0.048) (0.017) (0.013)

ΔSpend. 1932-37 0.003(0.004)

ΔRev. 1932-37 -0.001(0.008)

ΔTax. 1932-37 0.009(0.006)

Constitution 0.152 0.113 0.191 -0.070 0.033 0.079 0.111(0.178) (0.206) (0.152) (0.185) (0.127) (0.198) (0.166)

Referendum 0.428** 0.398** 0.268 -0.055 0.079 0.404** 0.427**(0.168) (0.167) (0.164) (0.208) (0.169) (0.169) (0.164)

BBR -0.036(0.145)

Rating: Aa 0.389**(0.178)

Rating: A 0.163(0.159)

Rating: Baa/Ba 0.251(0.257)

Constant -0.302 -0.507*** -0.042 -0.641*** -0.220 -0.458* -0.063(0.242) (0.170) (0.223) (0.166) (0.266) (0.232) (0.187)

Observations 48 48 48 36 48 43 45 48R-squared 0.343 0.332 0.279 0.518 0.313 0.464 0.238

Notes: Sales Tax 1930s is a binary variable equal to unity for the 28 states that levied a retail sales tax in the 1930s; Sales Tax:Permanent excludes the six states levying a temporary retail sales tax in the 1930s. Income Tax 1929, Income Tax 1940 and CorporateTax 1929 are indicators for the presence of those tax bases in 1929 or 1940. ΔInc 1929-33 is 100x the log change in real state per capitapersonal income from 1929 to 1933, with a mean value of -34. Debt 1929 is the state debt-to-income ratio in 1929 in percent, with amean value of 3.2 and a maximum value of 17.9. ΔSpend 1932-37,ΔRev. 1932-37 ΔTax. 1932-37 is 100x the log change in real stateper capita state government spending, total revenue and tax revenue, respectively, from 1932 to 1937. Constitution is a dummy variableequal to unity for states requiring a constitutional amendment to incur debt, Referendum is a dummy variable equal to unity for statesrequiring a referendum to incur debt, and BBR is a dummy variable taking the value unity for states with a balanced budget requirement.Rating is the General Obligation bond rating in 1937; omitted category is a Aaa-rating. Coefficients for regression specification (2)are marginal effects at the mean for each variable, and for a discrete change from 0 to 1 for binary dependent variables. Regression(6) excludes the five states with the highest 1929 debt-to-income ratios: Alabama, Arkansas, North Carolina, South Carolina, WestVirginia. Regression (4) is restricted to states that did not have an income tax in 1929. Statistical significance at the 1, 5, and 10 percentlevels is denoted by ***, **, and *, respectively. Robust standard errors have been used.

41

Figure 1: Tax Base Breadth

(a) Administrative Cost Function

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42

Figure 2: Number of U.S. State Governments with a Sales Tax

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Figure 3: Real State Per Capital Personal Income: 1929=100

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Notes: Sales Tax: Yes is the average for the 28 states that levied a retail sales tax in the 1930s, and Sales Tax: No is the averagefor the 20 states that did not; individual states are shown in grey. Nominal state per capita personal income data was convertedto real values using the U.S. GDP deflator. Sources: BEA; Due and Mikesell (1995); U.S. Department of Commerce (VariousIssues).

43

Figure 4: Revenue and Spending: By State Government

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Notes: Sales Tax: Yes is the 28 states that levied a retail sales tax in the 1930s, and Sales Tax: No is the 20 states thatdid not. Income is state per capita personal income. Nominal revenues and spending were converted to real values usingthe U.S. GDP deflator. Spending data are total state government cost payments for 1927-1937, and total state governmentexpenditures for 1942-1952. Sources: BEA, Due and Mikesell (1995), U.S. Department of Commerce (Various Issues).

44

Figure 5: Retail Sales Tax Adoption: By Percentage Change in Assessed Property Values

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Note: Sales Tax: No is the group of states that did not introduce a retail sales tax in the 1930s, Sales Tax: 1937 is the groupof states that had a retail sales tax in 1937. All of these retail sales tax bases ultimately became permanent. Each columnindicates the real percentage change from 1929-1937 in the assessed valuation of property subject to general property tax.California, Delaware, Pennsylvania and North Carolina did not levy property tax at the state government level in 1929, andare excluded from the figure; except for Delaware, these states levied a sales tax during the 1930s. Iowa, which experienced a158 percent increase, is also excluded from the figure. Sources: Due and Mikesell (1995), and U.S. Department of Commerce(Various Issues).

45

Figure 6: State Government Debt

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Notes: Sales Tax: Yes is the 28 states that levied a retail sales tax in the 1930s, and Sales Tax: No is the 20 states that didnot. Income is state per capita personal income. Debt is less sinking fund assets, and real debt is nominal debt deflated by theU.S. GDP deflator. Data shown for years available. Sources: BEA, Due and Mikesell (1995), U.S. Department of Commerce(Various Issues).

46

Figure 7: Tax Revenue Shares: 1932

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47